Not only is md5sum not proven to have equal dostribution, it is specifically known to not have equal distribution, only nearly equal distribution.

A hash function is any function that converts an arbitrary input size into a specific output size deterministically. No other requirements are there. A hash for a simple job could be just adding the ascii values together and give the output. Needless to say, that would not have an even distribution.

The hashes not being there isn’t particularly relevant within a hash function outputting a specific size. If your hash function is always 64 bits for example, the fact that you have 3/4th of them not exist means you should be operating as if its a 16 bit hash, not a 64 bit hash. If you still do this math based on the 64 bits outputted (2^64 boxes) you’d arrive at very inaccurate numbers.

This is valid on a single unlisted assumption: The hash function has equal distribution. If your has function ends by multipliying the has value by 4, for example, your number of possible boxes is 1/4th the otherwise expected value based on the size of the hash output